Teorija števil v kolobarjih polinomov nad končnimi obsegi : magistrsko delo
Kapus, Sergej, 1954-
Kolobar celih števil in kolobar ▫$A = \boldsymbol{F}[T]$▫ polinomov nad končnim obsegom ▫$\boldsymbol{F}$▫ imata veliko skupnih lastnosti. V magistrskem delu poudarimo paralele med njima. Pokažemo, ...da je ▫$A$▫ glavni kolobar, da vsebuje nešteto nerazcepnih elementov, končno mnogo enot in da je kvocientni kolobar ▫$A/fA$▫ po neničelnem idealu končen. Dokažemo analogije Eulerjevemu izreku, malemu Fermatovemu izreku in Wilsonovemu izreku iz klasične teorije števil. Definiramo analogijo Riemannove funkcije ▫$\zeta$▫ in z njo dokažemo polinomsko verzijo praštevilskega izreka. Vpeljemo analogije klasičnim aritmetičnim funkcijam, definiramo Dirichletove vrste in Dirichletov produkt. Dokažemo splošni recipročnostni zakon za potence stopnje ▫$d$▫. Definiramo Dirichletove karakterje po modulu ▫$m$▫ in Dirichletove ▫$L$▫-vrste. Z njimi dokažemo polinomsko verzijo Dirichletovega izreka o praštevilih v aritmetičnem zaporedju.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Ljubljana : [S. Kapus], 2005
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